Swirling Flow of a Viscoelastic Fluid With Free Surface: Part II — Numerical Analysis With Extended Marker-and-Cell Method

2004 ◽  
Author(s):  
Bo Yu ◽  
Jinjia Wei ◽  
Yasuo Kawaguchi
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Turbulence Model ◽  
Swirling Flow ◽  
Surfactant Solution ◽  
Secondary Flows ◽  
Surface Shape ◽  
Alternative Methods ◽  
Large Reynolds Number ◽  
Meridional Plane

In Part I [1], we presented the experimental results for swirling flows of water and cetyltrimethyl ammonium chloride (CTAC) surfactant solution in a cylindrical vessel with a rotating disk located at the bottom for a Reynolds number of around 4.3 × 104 based on the viscosity of solvent. For the large Reynolds number, violent irregular instantaneous secondary flows at the meridional plane were observed by use of a PIV system. Because of the limitations of our computer resources, we did not carry out DNS simulation for such a large Reynolds number. The LES and turbulence model are alternative methods, but a viscoelastic LES/turbulence model has not yet been developed for the surfactant solution. In this study, therefore, we limited our simulations to a laminar flow. The Marker-and-Cell (MAC) method proposed for Newtonian flow was extended to the viscoelastic flow to track the free surface, and the effects of Weissenberg number and Froude number on the flow pattern and surface shape were studied. Although the Reynolds number is much smaller than that of the experiment, the major experimental observations such as the inhibition of primary and secondary flows and the decrease of the dip of the free surface by the elasticity of the solution, were qualitatively reproduced in the numerical simulations.

Swirling Flow of a Viscoelastic Fluid With Free Surface—Part II: Numerical Analysis With Extended Marker-and-Cell Method

2005 ◽  
Vol 128 (1) ◽  
pp. 77-87 ◽  
Author(s):  
Bo Yu ◽  
Jinjia Wei ◽  
Yasuo Kawaguchi
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Turbulence Model ◽  
Surfactant Solution ◽  
Secondary Flows ◽  
Surface Shape ◽  
Alternative Methods ◽  
Large Reynolds Number ◽  
Cell Method ◽  
Marker And Cell Method

In Part I [Wei et al., 2004, 2004 ASME Int. Mech. Eng. Conference], we presented the experimental results for swirling flows of water and cetyltrimethyl ammonium chloride (CTAC) surfactant solution in a cylindrical vessel with a rotating disk located at the bottom for a Reynolds number of around 4.3×104 based on the viscosity of solvent. For the large Reynolds number, violent irregular instantaneous secondary flows at the meridional plane were observed by use of a particle image velocimetry system. Because of the limitations of our computer resources, we did not carry out direct numerical simulation for such a large Reynolds number. The LES and turbulence model are alternative methods, but a viscoelastic LES/turbulence model has not yet been developed for the surfactant solution. In this study, therefore, we limited our simulations to a laminar flow. The marker-and-cell method proposed for Newtonian flow was extended to the viscoelastic flow to track the free surface, and the effects of Weissenberg number and Froude number on the flow pattern and surface shape were studied. Although the Reynolds number is much smaller than that of the experiment, the major experimental observations, such as the inhibition of primary and secondary flows and the decrease of the dip of the free surface by the elasticity of the solution, were qualitatively reproduced in the numerical simulations.

Swirling Flow of a Viscoelastic Fluid With Free Surface—Part I: Experimental Analysis of Vortex Motion by PIV

2005 ◽  
Vol 128 (1) ◽  
pp. 69-76 ◽  
Author(s):  
Jinjia Wei ◽  
Fengchen Li ◽  
Bo Yu ◽  
Yasuo Kawaguchi
Keyword(s):  
Free Surface ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Vortex Motion ◽  
Surfactant Solution ◽  
Particle Image Velocimetry System ◽  
Meridional Plane ◽  
Cylindrical Wall ◽  
Rotating Disc ◽  
Solution Flow

The swirling flows of water and CTAC (cetyltrimethyl ammonium chloride) surfactant solutions (50-1000ppm) in an open cylindrical container with a rotating disc at the bottom were experimentally investigated by use of a double-pulsed PIV (particle image velocimetry) system. The flow pattern in the meridional plane for water at the present high Reynolds number of 4.3×104 differed greatly from that at low Reynolds numbers, and an inertia-driven vortex was pushed to the corner between the free surface and the cylindrical wall by a counter-rotating vortex caused by vortex breakdown. For the 1000ppm surfactant solution flow, the inertia-driven vortex located at the corner between the bottom and the cylindrical wall whereas an elasticity-driven reverse vortex governed the majority of the flow field. The rotation of the fluid caused a deformation of the free surface with a dip at the center. The dip was largest for the water case and decreased with increasing surfactant concentration. The value of the dip was related to determining the solution viscoelasticity for the onset of drag reduction.

Swirling Flow of a Viscoelastic Fluid With Free Surface: Part I — Experimental Analysis of Vortex Motion by PIV

2004 ◽  
Author(s):  
Jinjia Wei ◽  
Fengchen Li ◽  
Bo Yu ◽  
Yasuo Kawaguchi
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Particle Image Velocimetry System ◽  
Meridional Plane ◽  
Cylindrical Wall ◽  
Rotating Disc ◽  
Solution Flow ◽  
Surfactant Solutions

The swirling flows of water and CTAC (cetyltrimethyl ammonium chloride) surfactant solutions in an open cylindrical container with a rotating disc at the bottom were experimentally investigated by use of a double-pulsed PIV (particle image velocimetry) system. The mass concentrations of CTAC solutions were in the range of 50–1000 ppm, and the Reynolds number based on angular velocity, kinematic viscosity of water and radius of rotating disc was fixed at 4.3 × 104. The aspect ratio of the height of the liquid filled into the cylindrical vessel to the radius of the vessel was set to 1.0. The secondary flow patterns in the meridional plane and the tangential velocities were obtained. The flow pattern in the meridional plane for water at the present high Reynolds number differed greatly from that at low Reynolds numbers, and an inertia-driven vortex was pushed to the corner between the free surface and the cylindrical wall by a counter-rotating vortex caused by vortex breakdown. For the 1000-ppm surfactant solution flow, the inertia-driven vortex located at the corner between the bottom and the cylindrical wall whereas an elasticity-driven reverse vortex governed the majority of the flow field. The radial distributions of the time-averaged tangential velocities also differed for water and surfactant solutions. The rotation of the fluid caused a deformation of the free surface with a dip at the center. The dip was largest for the water case and decreased with increasing surfactant concentration.

Capability of Two Equation k-ω Turbulence Model to Predict Pressure Values on “Quarter-Circular” Object

2016 ◽  
Vol 837 ◽  
pp. 209-213
Author(s):  
Juraj Kralik ◽  
Olga Hubova ◽  
Lenka Konecna
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Turbulence Model ◽  
Fluid Dynamic ◽  
Convergence Time ◽  
Large Reynolds Number ◽  
Mean Values ◽  
Circular Object ◽  
Basic Characteristics ◽  
Property Changes

Turbulence is a flow regime characterized by chaotic property changes. Randomness, fluctuations, vorticity and large Reynolds number (Re) are the basic characteristics of turbulent flows. In this contribution is Computer Fluid Dynamic simulation of air-flow over an obstacle in shape of “quarter-circular” object compared to the data from previous work. This comparison is focused on mean values of pressure in 16 selected points at different elevations. k-ω turbulence model performed well (convergence, time, CPU) and the overall error is 13.61 %.

Three-Dimensional Navier–Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k–ε Turbulence Model

1992 ◽  
Vol 114 (3) ◽  
pp. 627-642 ◽  
Author(s):  
R. F. Kunz ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Secondary Flows ◽  
Quality Data ◽  
Navier Stokes ◽  
Evaluation Procedure ◽  
Pressure Probe ◽  
Time Step

An explicit, three-dimensional, coupled Navier–Stokes/k–ε technique has been developed and successfully applied to complex internal flow calculations. Several features of the procedure, which enable convergent and accurate calculation of high Reynolds number two-dimensional cascade flows, have been extended to three dimensions, including a low Reynolds number compressible form of the k–ε turbulence model, local time-step specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators. A flux evaluation procedure, which eliminates the finite difference metric singularity at leading and trailing edges on H- and C-grids, is presented. The code is used to predict the pressure distribution, primary velocity, and secondary flows in an incompressible, turbulent curved duct flow for which CFD validation quality data are available. Also, a subsonic compressor rotor passage, for which detailed laser, rotating hot-wire, and five-hole pressure probe measurements have been made is computed. Detailed comparisons between predicted and measured core flow and near-wall velocity profiles, wake profiles, and spanwise mixing effects downstream of the rotor passage are presented for this case. It is found that the technique provides accurate and convergent engineering simulation of these complex turbulent flows.

Three-Dimensional Navier-Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k-ε Turbulence Model

1991 ◽  
Author(s):  
R. F. Kunz ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Secondary Flows ◽  
Three Dimensions ◽  
Quality Data ◽  
Navier Stokes ◽  
Evaluation Procedure ◽  
Pressure Probe

An explicit, three-dimensional, coupled Navier-Stokes/k-ε technique has been developed and successfully applied to complex internal flow calculations. Several features of the procedure, which enable convergent and accurate calculation of high Reynolds number two-dimensional cascade flows have been extended to three-dimensions, including a low Reynolds number compressible form of the k-ε turbulence model, local timestep specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators. A flux evaluation procedure which eliminates the finite difference metric singularity, at leading and trailing edges, on H- and C-grids, is presented. The code is used to predict the pressure distribution, primary velocity and secondary flows in an incompressible, turbulent curved duct flow for which CFD validation quality data is available. Also, a subsonic compressor rotor passage, for which detailed laser, rotating hot-wire and five-hole pressure probe measurements have been made is computed. Detailed comparisons between predicted and measured core flow and near wall velocity profiles, wake profiles, and spanwise mixing effects downstream of the rotor passage are presented for this case. It is found that the technique provides accurate and convergent engineering simulation of these complex turbulent flows.

scholarly journals Design of a Novel μ-Mixer

2017 ◽  
Author(s):  
Athanasios G. Kanaris ◽  
Aikaterini A. Mouza
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Swirling Flow ◽  
Numerical Data ◽  
Secondary Flows ◽  
Design Parameters ◽  
Mixing Efficiency ◽  
Geometrical Parameters ◽  
Straight Tube ◽  
Propeller Blades

In this work the efficiency of a new μ-mixer design is investigated. As in this type of devices the Reynolds number is low, mixing is diffusion dominated and it can be enhanced by creating secondary flows. In this study we propose the introduction of helical inserts into a straight tube to create swirling flow. The influence of the insert’s geometrical parameters (pitch and length of the propeller blades) and of the Reynolds number on the mixing efficiency and on the pressure drop are numerically investigated. The mixing efficiency of the device is assessed by calculating a number, i.e. the Index of Mixing Efficiency that quantifies the uniformity of concentration at the outlet of the device. The influence of the design parameters on the mixing efficiency is assessed by performing a series of “computational” experiments, in which the values of the parameter are selected using DOE methodology. Finally using the numerical data, appropriate design equations are formulated, which, for given values ​​of the design parameters, can estimate with reasonable accuracy both the mixing efficiency and the pressure drop of the proposed mixing device.

Experimental Study of Swirling Flow of a Viscoelastic Fluid With Deformed Free Surface

2006 ◽  
Author(s):  
Feng-Chen Li ◽  
Masamichi Oishi ◽  
Yasuo Kawaguchi ◽  
Nobuyuki Oshima ◽  
Marie Oshima
Keyword(s):  
Free Surface ◽  
Water Flow ◽  
Viscoelastic Fluid ◽  
Swirling Flow ◽  
Solution Concentration ◽  
Force Balance ◽  
Meridional Plane ◽  
Solution Flow ◽  
Secondary Velocity ◽  
Cetyltrimethyl Ammonium

An experimental investigation was performed on the swirling flow of viscoelastic fluid with deformed free surface in a cylindrical container driven by the constantly rotating bottom wall. The tested fluid was an aqueous solution of CTAC (cetyltrimethyl ammonium chloride), which is a cationic surfactant. Water, 40ppm, 60ppm and 200ppm CTAC solution flows were tested at Froude numbers ranging from 2.59 to 16.3. PIV was used to measure the secondary velocity field in the meridional plane and the deformed free-surface level was extracted from the PIV images. At a similar Froude number, the depth of the dip formed at the center region of the free surface was decreased for CTAC solution flow compared with water flow. The inertia-driven vortex at the up-right corner in the meridional plane becomes more and more weakened with increase of the solution concentration or viscoelasticity. Through analyzing the overall force balance compared with water flow, the first normal stress difference or the weak viscoelasticity was estimated for the dilute CTAC solution flows.

Axisymmetric rotating flow with free surface in a cylindrical tank

2018 ◽  
Vol 861 ◽  
pp. 796-814 ◽  
Author(s):  
Wen Yang ◽  
Ivan Delbende ◽  
Yann Fraigneau ◽  
Laurent Martin Witkowski
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Azimuthal Velocity ◽  
Meridional Plane ◽  
Cylindrical Tank ◽  
Aspect Ratios ◽  
Steady Solutions

The flow induced by a disk rotating at the bottom of a cylindrical tank is characterised using numerical techniques – computation of steady solutions or time-averaged two-dimensional and three-dimensional direct simulations – as well as laser-Doppler velocimetry measurements. Axisymmetric steady solutions reveal the structure of the toroidal flow located at the periphery of the central solid body rotation region. When viewed in a meridional plane, this flow cell is found to be bordered by four layers, two at the solid boundaries, one at the free surface and one located at the edge of the central region, which possesses a sinuous shape. The cell intensity and geometry are determined for several fluid-layer aspect ratios; the flow is shown to depend very weakly on Froude number (associated with surface deformation) or on Reynolds number if sufficiently large. The paper then focuses on the high Reynolds number regime for which the flow has become unsteady and three-dimensional while the surface is still almost flat. Direct numerical simulations show that the averaged flow shares many similarities with the above steady axisymmetric solutions. Experimental measurements corroborate most of the numerical results and also allow for the spatio-temporal characterisation of the fluctuations, in particular the azimuthal structure and frequency spectrum. Mean azimuthal velocity profiles obtained in this transitional regime are eventually compared to existing theoretical models.

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